P
US7536366B2ExpiredUtilityPatentIndex 62

Contingency table estimation via sketches

Assignee: MICROSOFT CORPPriority: Sep 15, 2005Filed: Dec 28, 2005Granted: May 19, 2009
Est. expirySep 15, 2025(expired)· nominal 20-yr term from priority
Inventors:CHURCH KENNETH WARDLI PING
G06F 16/328Y10S707/99935G06F 16/93G06F 2216/03G06F 16/38Y10S707/99936
62
PatentIndex Score
4
Cited by
4
References
10
Claims

Abstract

Systems and methods that enhance estimate(s) of features (e.g., word associations), via employing a sampling component (e.g., sketches) that facilitates computations of sample contingency tables, and designates occurrences (or absence) of features in data (e.g., words in document lists). The sampling component can further include a contingency table generator and an estimation that employs a likelihood argument (e.g., partial likelihood, maximum likelihood, and the like) to estimate features/word pair(s) associations in the contingency tables.

Claims

exact text as granted — not AI-modified
1. A computer implemented system comprising the following computer executable components:
 a memory; 
 a processor that executes the following software components; 
 a sampling component that employs sketches to facilitate generation of contingency tables and forms a sample of data; and 
 an estimation component that employs a probabilistic argument to locate a most likely contingency table for the sample; 
 wherein the contingency tables comprise a sample intersection cell (a s ) that is equal to an intersection cell (a) multiplied by a sampling rate (s); 
 wherein the processor finds and outputs to a computer display, estimates on word pair associations in searching document lists on a computer; and 
 wherein the sketches employed to facilitate generation of the contingency tables comprise sketches K 1 , K 2 , and 
 
     
       
         
           
             
               
                 D 
                 s 
               
               = 
               
                 min 
                 ⁢ 
                 
                     
                 
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                   { 
                   
                     
                       K 
                       
                         1 
                         ⁢ 
                         
                           ( 
                           
                             k 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       K 
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             k 
                             2 
                           
                           ) 
                         
                       
                     
                   
                   } 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 k 
                 1 
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                 - 
                 
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                     { 
                     
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                       : 
                       
                         
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                               ( 
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                    
                 
               
             
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                 ′ 
               
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                     { 
                     
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                       : 
                       
                         
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                             2 
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                               ( 
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                           s 
                         
                       
                     
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                    
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 a 
                 s 
               
               = 
               
                  
                 
                   
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                     1 
                   
                   ⋂ 
                   
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                  
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 b 
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               = 
               
                 
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                 - 
                 
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             , 
             
               
 
             
             ⁢ 
             
               
                 c 
                 s 
               
               = 
               
                 
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                 - 
                 
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             , 
             
               
 
             
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                 d 
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               = 
               
                 
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                 - 
                 
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                   s 
                 
                 - 
                 
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                     c 
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                   . 
                 
               
             
           
         
       
       wherein the most likely contingency table is determined via defining a maximum likelihood estimation as 
     
     
       
         
           
             
               
                 
                   
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       and a closed form solution is presented in the form of 
     
     
       
         
           
             
               
                 a 
                 ^ 
               
               
                 MLE 
                 , 
                 a 
               
             
             = 
             
               
                 
                   
                     
                       
                         
                           
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                                     ( 
                                     
                                       
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                           s 
                         
                       
                       + 
                       
                         b 
                         s 
                       
                       + 
                       
                         c 
                         s 
                       
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
   
   
     2. The computer implemented system of  claim 1 , the estimation component further comprising a maximum likelihood estimation. 
   
   
     3. The computer implemented system of  claim 2 , further comprising a stopping rule that is based on the likelihood estimation. 
   
   
     4. The computer implemented system of  claim 1 , further comprising an artificial intelligence component that facilitates estimation of word associations, via utilizing an automatic classification system that learns explicitly or implicitly when the contingency tables should be generated, wherein the classification system employs a probabilistic and/or statistical-based analysis to infer an action that a user desires to be automatically performed. 
   
   
     5. A computer implemented method comprising the following computer executable acts:
 sampling a collection of data to form a sample space; 
 computing a contingency table within the sample space for features that require association estimation; 
 employing sketches to facilitate generation of the contingency table and to form a sample of data; 
 employing a probabilistic argument on the contingency table to determine the most likely contingency table; 
 employing a linear relation between a sample intersection cell and a sampling rate, wherein the contingency table comprises a sample intersection cell (a s ) that is equal to an intersection cell (a) multiplied by a sampling rate (s); 
 finding and outputting estimates on word pair associations in searching document lists on a computer; 
 employing 
 
     
       
         
           
             
               
                 D 
                 s 
               
               = 
               
                 min 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   { 
                   
                     
                       K 
                       
                         1 
                         ⁢ 
                         
                           ( 
                           
                             k 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       K 
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             k 
                             2 
                           
                           ) 
                         
                       
                     
                   
                   } 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 k 
                 1 
                 ′ 
               
               = 
               
                 
                   k 
                   1 
                 
                 - 
                 
                    
                   
                     { 
                     
                       j 
                       : 
                       
                         
                           K 
                           
                             1 
                             ⁢ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         > 
                         
                           D 
                           s 
                         
                       
                     
                     } 
                   
                    
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 k 
                 2 
                 ′ 
               
               = 
               
                 
                   k 
                   2 
                 
                 - 
                 
                    
                   
                     { 
                     
                       j 
                       : 
                       
                         
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                             2 
                             ⁢ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         > 
                         
                           D 
                           s 
                         
                       
                     
                     } 
                   
                    
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 a 
                 s 
               
               = 
               
                  
                 
                   
                     K 
                     1 
                   
                   ⋂ 
                   
                     K 
                     2 
                   
                 
                  
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 b 
                 s 
               
               = 
               
                 
                   k 
                   1 
                   ′ 
                 
                 - 
                 
                   a 
                   s 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 c 
                 s 
               
               = 
               
                 
                   k 
                   2 
                   ′ 
                 
                 - 
                 
                   a 
                   s 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 d 
                 s 
               
               = 
               
                 
                   D 
                   s 
                 
                 - 
                 
                   a 
                   s 
                 
                 - 
                 
                   b 
                   s 
                 
                 - 
                 
                   c 
                   s 
                 
               
             
           
         
       
     
     for sketches K 1 , K 2 ;
 determining the most likely contingency table via defining a maximum likelihood estimation as 
 
     
       
         
           
             
               
                 P 
                 ⁡ 
                 
                   ( 
                   
                     
                       a 
                       s 
                     
                     , 
                     
                       b 
                       s 
                     
                     , 
                     
                       c 
                       
                         s 
                         ⁢ 
                         
                             
                         
                       
                     
                     , 
                     
                       
                         
                           d 
                           s 
                         
                         | 
                         
                           D 
                           s 
                         
                       
                       ; 
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                 ∝ 
                 
                   
                     
                       
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                       ⁡ 
                       
                         ( 
                         
                           
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                           - 
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                         ) 
                       
                     
                     
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                       s 
                     
                   
                   - 
                   
                     
                       
                         ( 
                         
                           
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                             2 
                           
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                         c 
                         s 
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
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                           - 
                           
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                             1 
                           
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                             2 
                           
                           + 
                           a 
                         
                         ) 
                       
                       
                         d 
                         s 
                       
                     
                   
                 
               
             
             ; 
           
         
       
       and presenting a closed form solution in form of 
     
     
       
         
           
             
               
                 a 
                 ^ 
               
               
                 MLE 
                 , 
                 a 
               
             
             = 
             
               
                 
                   
                     
                       
                         
                           
                             f 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   a 
                                   s 
                                 
                               
                               + 
                               
                                 c 
                                 s 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             f 
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   a 
                                   s 
                                 
                               
                               + 
                               
                                 b 
                                 s 
                               
                             
                             ) 
                           
                         
                         - 
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     f 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           a 
                                           s 
                                         
                                       
                                       + 
                                       
                                         c 
                                         s 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
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                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
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                                       + 
                                       
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                             2 
                           
                           + 
                           
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                             ⁢ 
                             
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                   2 
                   ⁢ 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                           a 
                           s 
                         
                       
                       + 
                       
                         b 
                         s 
                       
                       + 
                       
                         c 
                         s 
                       
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
   
   
     6. The method of  claim 5  further comprising employing a maximum likelihood estimation. 
   
   
     7. The method of  claim 5  further comprising employing variances based on document frequencies. 
   
   
     8. The method of  claim 5  further comprising representing a partial likelihood as 
     
       
         
           
             
               P 
               ⁡ 
               
                 ( 
                 
                   
                     a 
                     s 
                   
                   , 
                   
                     b 
                     s 
                   
                   , 
                   
                     c 
                     s 
                   
                   , 
                   
                     
                       
                         d 
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                       | 
                       
                         D 
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                     ; 
                     a 
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
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                   ) 
                 
               
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           
                             a 
                           
                         
                         
                           
                             
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                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 f 
                                 1 
                               
                               - 
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                               b 
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                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
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                                 2 
                               
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                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               D 
                               - 
                               
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                                 1 
                               
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                               + 
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                     ( 
                     
                       
                         
                           D 
                         
                       
                       
                         
                           
                             D 
                             s 
                           
                         
                       
                     
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
   
   
     9. The method of  claim 8  further comprising presenting a solution as: 
     
       
         
           
             
               
                 
                   
                     g 
                     ⁡ 
                     
                       ( 
                       a 
                       ) 
                     
                   
                   = 
                   
                     
                       a 
                       
                         a 
                         - 
                         
                           a 
                           s 
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           f 
                           1 
                         
                         - 
                         a 
                         + 
                         1 
                         - 
                         
                           b 
                           s 
                         
                       
                       
                         
                           f 
                           1 
                         
                         - 
                         a 
                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
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                           2 
                         
                         - 
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                         + 
                         1 
                         - 
                         
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                           s 
                         
                       
                       
                         
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                           2 
                         
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                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         D 
                         - 
                         
                           f 
                           1 
                         
                         - 
                         
                           f 
                           2 
                         
                         + 
                         a 
                       
                       
                         D 
                         - 
                         
                           f 
                           1 
                         
                         - 
                         
                           f 
                           2 
                         
                         + 
                         a 
                         - 
                         
                           d 
                           s 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   1. 
                 
               
             
           
         
       
     
   
   
     10. A computer implemented system comprising the following computer executable components:
 means for sampling a collection of documents to form a sample space; 
 means for computing a contingency table within the sample space; 
 means for employing sketches to facilitate generation of the contingency table and to form a sample of data; 
 means for employing a probabilistic argument on the contingency table to determine the most likely contingency table; 
 means for employing a linear relation between a sample intersection cell and a sampling rate, wherein the contingency table comprises a sample intersection cell (a s ) that is equal to an intersection cell (a) multiplied by a sampling rate (s); 
 means for finding and outputting estimates on word pair associations in using the sample intersection cell and the sampling rate; 
 means for employing 
 
     
       
         
           
             
               
                 
                   
                     
                       D 
                       s 
                     
                     = 
                       
                     ⁢ 
                     
                       min 
                       ⁢ 
                       
                         { 
                         
                           
                             K 
                             
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   k 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           , 
                           
                             K 
                             
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   k 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                     
                   
                   , 
                 
               
             
             
               
                 
                   
                     
                       k 
                       1 
                       ′ 
                     
                     = 
                       
                     ⁢ 
                     
                       
                         k 
                         1 
                       
                       - 
                       
                          
                         
                           { 
                           
                             j 
                             : 
                             
                               
                                 K 
                                 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     j 
                                     ) 
                                   
                                 
                               
                               > 
                               
                                 D 
                                 s 
                               
                             
                           
                           } 
                         
                          
                       
                     
                   
                   , 
                   
                     
                       k 
                       2 
                       ′ 
                     
                     = 
                     
                       
                         k 
                         2 
                       
                       - 
                       
                          
                         
                           { 
                           
                             j 
                             : 
                             
                               
                                 K 
                                 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     j 
                                     ) 
                                   
                                 
                               
                               > 
                               
                                 D 
                                 s 
                               
                             
                           
                           } 
                         
                          
                       
                     
                   
                   , 
                 
               
             
             
               
                 
                   
                     
                       a 
                       s 
                     
                     = 
                       
                     ⁢ 
                     
                        
                       
                         
                           K 
                           1 
                         
                         ⋂ 
                         
                           K 
                           2 
                         
                       
                        
                     
                   
                   , 
                   
                     
                       b 
                       s 
                     
                     = 
                     
                       
                         k 
                         1 
                         ′ 
                       
                       - 
                       
                         a 
                         s 
                       
                     
                   
                   , 
                   
                     
                       c 
                       s 
                     
                     = 
                     
                       
                         k 
                         2 
                         ′ 
                       
                       - 
                       
                         a 
                         s 
                       
                     
                   
                   , 
                   
                     
                       d 
                       s 
                     
                     = 
                     
                       
                         D 
                         s 
                       
                       - 
                       
                         a 
                         s 
                       
                       - 
                       
                         b 
                         s 
                       
                       - 
                       
                         c 
                         s 
                       
                     
                   
                 
               
             
           
         
       
     
     for sketches K1, K2;
 means for determining the most likely contingency table via defining a maximum likelihood estimation as 
 
     
       
         
           
             
               
                 P 
                 ⁡ 
                 
                   ( 
                   
                     
                       a 
                       s 
                     
                     , 
                     
                       b 
                       s 
                     
                     , 
                     
                       c 
                       s 
                     
                     , 
                     
                       
                         
                           d 
                           s 
                         
                         | 
                         
                           D 
                           s 
                         
                       
                       ; 
                       a 
                     
                     , 
                     r 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         
                           
                             D 
                             s 
                           
                         
                       
                       
                         
                           
                             
                               a 
                               s 
                             
                             , 
                             
                               b 
                               s 
                             
                             , 
                             
                               c 
                               s 
                             
                             , 
                             
                               d 
                               s 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         a 
                         D 
                       
                       ) 
                     
                     
                       a 
                       s 
                     
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         b 
                         D 
                       
                       ) 
                     
                     
                       b 
                       s 
                     
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         c 
                         D 
                       
                       ) 
                     
                     
                       c 
                       s 
                     
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         d 
                         D 
                       
                       ) 
                     
                     
                       d 
                       s 
                     
                   
                 
                 ∝ 
                 
                   
                     
                       
                         a 
                         
                           a 
                           s 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             f 
                             1 
                           
                           - 
                           a 
                         
                         ) 
                       
                     
                     
                       b 
                       s 
                     
                   
                   - 
                   
                     
                       
                         ( 
                         
                           
                             f 
                             2 
                           
                           - 
                           a 
                         
                         ) 
                       
                       
                         c 
                         s 
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           D 
                           - 
                           
                             f 
                             1 
                           
                           - 
                           
                             f 
                             2 
                           
                           + 
                           a 
                         
                         ) 
                       
                       
                         d 
                         s 
                       
                     
                   
                 
               
             
             ; 
           
         
       
     
     and means for presenting a closed form solution in form of 
     
       
         
           
             
               
                 a 
                 ^ 
               
               
                 MLE 
                 , 
                 a 
               
             
             = 
             
               
                 
                   
                     
                       
                         
                           
                             f 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   a 
                                   s 
                                 
                               
                               + 
                               
                                 c 
                                 s 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             f 
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   a 
                                   s 
                                 
                               
                               + 
                               
                                 b 
                                 s 
                               
                             
                             ) 
                           
                         
                         - 
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     f 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           a 
                                           s 
                                         
                                       
                                       + 
                                       
                                         c 
                                         s 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     f 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           a 
                                           s 
                                         
                                       
                                       + 
                                       
                                         b 
                                         s 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             4 
                             ⁢ 
                             
                               f 
                               1 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                             ⁢ 
                             
                               b 
                               s 
                             
                             ⁢ 
                             
                               c 
                               s 
                             
                           
                         
                       
                     
                   
                 
                 
                   2 
                   ⁢ 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                           a 
                           s 
                         
                       
                       + 
                       
                         b 
                         s 
                       
                       + 
                       
                         c 
                         s 
                       
                     
                     ) 
                   
                 
               
               .

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